We present experiments studying the coherent motion of atoms in crystals made from on and off resonant light. The experiments confirm that inside the light-field atoms fulfilling the Bragg condition form a standing matter wave pattern. As a consequence we observed anomalous transmission of atoms through resonant light fields.
Tailored complex potentials for atoms can be made of two overlapping standing light waves, one on resonance and one far detuned. The observed diffraction asymmetry of Bragg diffraction of such light structures is due to a corresponding asymmetry of the Fourier components of the potential. In crystal physics this is known as a violation of Friedel's law. [S0031-9007(97) PACS numbers: 61.12.Bt It is often found that concepts of photon optics can be adapted to matter-wave optics. In our article we choose the conjugate approach. We use the simplicity of the interaction between light and matter waves to design complex periodic potentials for the matter waves and reveal optical concepts. As an example, we investigate a violation of Friedel's law due to fundamental optical principles in a very controlled system.Typically, diffraction phenomena are invariant under an inversion of the crystal, even when the elementary cell of the crystal possesses no symmetry. This empirical rule is generally referred to as Friedel's law [1]. However, violations of this rule are known from diffraction experiments of x rays or electrons at solid state crystals [2], for example, due to the presence of "anomalous" (absorptive) scatterers. In this Letter we present a violation of Friedel's law in a very different system, where atomic matter waves are diffracted at specially designed "crystals" of light [3,4]. The diffraction asymmetry is due to the interaction of both "normal" and anomalous scattering at superposed refractive and absorptive subcrystals, respectively [5]. This mechanism even works although our light crystal obviously cannot be really absorptive for the atoms, but only changes their internal state.In our experiment ( Fig. 1), we detect atom intensities depending on the atom's incidence angle at the light crystals, and their diffraction angle. In the case of spatial coincidence between the refractive and the absorptive parts of the crystals we obtain symmetric diffraction, as shown in Fig. 1(b). This corresponds to the normal situation in solid state crystals, where Friedel's law is obeyed. However, a violation of Friedel's law is demonstrated in Figs. 1(a) and 1(c), where Bragg diffraction is dominant in one direction. There, the absorptive and refractive index parts of the crystals are arranged such that they are out of phase by 6p͞2.In the remainder of this Letter, we will show that this diffraction asymmetry can be understood by evaluating the Fourier composition of the resulting complex potential, and employing dynamical diffraction theory. This means specifically that the effect of the total crystal potential cannot be separated into the individual actions of its components. However, in the weak diffraction limit a more intuitive picture can be justified, which is presented in the following.The asymmetry can be understood as an interference effect between diffraction at refractive and absorptive "subcrystals" spatially displaced with respect to each other (Fig. 2). Generally, there is a p͞2 phase shift even between wa...
We build amplitude, i.e., absorptive masks, for neutral atoms using light, reversing the roles of light and atoms as compared to conventional optics. These masks can be used both to create and to probe spatially well-defined atomic distributions. The resolution of these masks can be significantly better than the optical wavelength. Applications range from atom lithography to fundamental atom optical experiments.
Temporal light modulation methods which are of great practical importance in optical technology, are emulated with matter waves. This includes generation and tailoring of matter-wave sidebands, using amplitude and phase modulation of an atomic beam. In the experiments atoms are Bragg diffracted at standing light fields, which are periodically modulated in intensity or frequency. This gives rise to a generalized Bragg situation under which the atomic matter waves are both diffracted and coherently shifted in their de Broglie frequency. In particular, we demonstrate creation of complex and non-Hermitian matter-wave modulations. One interesting case is a potential with a time-dependent complex helicity ͓Vϰexp(it)͔, which produces a purely lopsided energy transfer between the atoms and the photons, and thus violates the usual symmetry between absorption and stimulated emission of energy quanta. Possible applications range from atom cooling over advanced atomic interferometers to a new type of mass spectrometer.
Atoms in light crystals formed by a standing light wave are a model system to study the propagation of matter waves in periodic potentials. The encountered phenomena can be described by dynamical diffraction theory which has been extensively studied for x-ray, electron, and neutron scattering from solid state crystals. In this paper we show that an atomic de Broglie wave traversing a standing light wave allows investigation of predictions of dynamical diffraction theory which were previously experimentally not accessible. We present standard diffraction efficiency characterizations for pure absorptive and pure refractive crystals. Additionally we were able to measure directly the total atomic wave field formed inside a refractive and an absorptive crystal and to confirm the predicted absolute position of the atomic wave field with respect to the lattice planes. By superposing two standing light waves of different frequency we tailored a new kind of crystal potential where Friedel's law about usual diffraction symmetries is maximally violated. ͓S1050-2947͑99͒02207-6͔
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.